Based on Exploratory Data Analysis (EDA), we employed various time series forecasting models, including the Prophet Model, ETS Model, and XGB Regressor Model, to predict the future values of our target variables.
Prior to model development, we conducted the Augmented Dickey-Fuller(ADF) test to assess the stationarity of our time series data. The consistently low p-values (< 0.05) across all target variables resulted in the rejection of the null hypothesis, affirming the stationarity of the data. This pivotal finding enhances the reliability of subsequent analyses and forecasts.
Additionally, Time Series Decomposition was performed, unveiling distinctive patterns for each product category. Inside sales exhibited a seasonal trend with summer peaks, an upward trajectory over the past year, and relatively small residuals. Similarly, food sales displayed a comparable pattern with an underlying upward trend and limited residuals. Diesel sales revealed a significant spike in 2022, a discernible trend, and a random residual pattern, while unleaded prices showcased seasonal fluctuations with an upward trend and unpredictable residuals. These decompositions provided valuable insights into each product's sales dynamics, emphasizing seasonal trends, long-term trajectories, and variations unaccounted for by trends or seasonality.
To assess model performance, we employed diverse metrics such as MAE, MSE, and RMSE, aiming to identify the model that achieved the highest accuracy and effectively forecasted the values.
PROPHET Model:¶
The performance evaluation of the Prophet model, post hyperparameter tuning, revealed noteworthy insights. The model demonstrated its best accuracy with the lowest Mean Absolute Error (MAE) of 281.06 and RMSE value 354.7 for the Food Sales target variable, showcasing a high precision in predicting future values. In contrast, the Diesel Sales target variable exhibited the highest MAE of 1543.6 and RMSE 2350.4, indicating a relatively lower accuracy compared to other variables.
For Inside Sales and Unleaded targets, the MAE values are around 820 to 860 and RMSE slightly greater than 1000, suggesting a moderate level of accuracy in forecasting. This variance in MAE and RMSE values implies that the model performs exceptionally well for Food Sales, moderately for Inside Sales and Unleaded, and relatively less accurately for Diesel Sales.
The observed MAE and RMSE discrepancies point towards potential areas for improvement, emphasizing the need for further exploration in hyperparameter tuning. The model's performance could likely be enhanced by experimenting with additional combinations of hyperparameter settings to fine-tune its predictive capabilities. This iterative refinement process could contribute to achieving more accurate and reliable forecasts across all target variables.
ETS Model:¶
The implementation of the Exponential Triple Smoothing (ETS) model brought notable enhancements in performance metrics, particularly for Diesel and Unleaded sales forecasting. The RMSE values for Diesel and Unleaded improved significantly to 1707.04 and 687.57, respectively, showcasing a marked enhancement compared to the Prophet model. This implies that the ETS model provides more accurate predictions for Diesel and Unleaded sales.
However, the ETS model did not perform as effectively for Inside Sales and Food Sales, as evidenced by slightly increased RMSE values. The RMSE values for Inside Sales and Food Sales are 1122.71 and 396.70, respectively. While the model improvements are evident for Diesel and Unleaded, the efficacy of the ETS model for Inside Sales and Food Sales appears to be less pronounced, suggesting that these specific variables may require further refinement or alternative modeling approaches.
XGB Regressor¶
The integration of the XGB Regressor model resulted in substantial improvements across all performance metrics for the target variables. Notably, the Root Mean Squared Error (RMSE) values for Inside Sales, Food Sales, Diesel, and Unleaded are recorded at 901.7, 317.3, 1258.9, and 988.4, respectively. These values represent a significant enhancement compared to the Prophet Model and ETS Model, signifying the XGB Regressor's superior predictive accuracy.
The substantial reduction in RMSE values highlights the effectiveness of the XGB Regressor in providing more precise forecasts for all target variables. Consequently, the XGB Regressor emerges as the preferred model among the compared alternatives Prophet and ETS demonstrating its superior performance in predicting the sales trends for Inside Sales, Food Sales, Diesel, and Unleaded.
